A recent change in law means the trust now receives money directly from the Commonwealth in the form of a subsidy. This, it is suggested, puts him in breach of section 44(v) of the Constitution.

That section prohibits members of Parliament from having "any direct or indirect pecuniary interest in any agreement with the Public Service of the Commonwealth".

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It appears the government has asked the Solicitor General to look into Mr Dutton's eligibility.

Leading constitutional expert Professor Anne Twomey of Sydney University said the outcome of any High Court case would depend on the facts, and specifically the arrangement between the childcare centres and the Commonwealth.

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A key question, she said, would be: "Is it simply a case of legislation providing for the payments or is there an agreement between the childcare centres and the Commonwealth that accredits the childcare centres so that they are able to receive the payments?

"If [Mr] Dutton had a pecuniary interest in such an agreement, it may be sufficient to trigger the s44 qualification."

She said it may come down to whether the court regards laws governing subsidies as "of general application" which entitle all childcare centres to the same outcomes.

"The question in that case would be if there was still some kind of prohibition due to a potential conflict of interest."

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She said one test that had been applied by the High Court was whether "a person might conceivably prefer their own financial interests over their public duties."

Professor Twomey noted that in the most recent case on section 44 (5) ? Family First senator Bob Day was ruled ineligible in 2017 because he held a pecuniary interest in the lease for his electorate office ? the High Court judges "weren't terribly sympathetic to the politicians".

"They saw the provision as there to protect the public interest from politicians who might conceivably prefer their private financial interests over their duty to the public interest.

"It is not inconceivable that if all the ducks line up in terms of the facts and the constitutional interpretation, Mr Dutton could be in serious strife. But we really need to know the full facts before reaching a judgment."

Liberal MP Peter Dutton during a division at Parliament House in Canberra on Thursday 23 August 2018. fedpol Photo: Alex Ellinghausen Alex Ellinghausen

Professor Anne Twomey said any High Court case would depend on the facts, and specifically the arrangement between the childcare centres and the Commonwealth. Supplied